A degree theory for a class of mappings of monotone type in Orlicz- Sobolev spaces. (English) Zbl 0821.47044
Annales Academiæ Scientiarum Fennicæ. Series A I. Mathematica. Dissertationes. 97. Helsinki: Acad. Scientiarum Fennica. 68 p. (1994).
In 1912 L. E. J. Brouwer constructed the classical degree for continuous mappings from a bounded open subset of \(\mathbb{R}^ n\) into \(\mathbb{R}^ n\). In 1934 Leray and Schauder generalized the degree for the class of compact perturbations of identity in infinite-dimensional Banach spaces. Since then, some interesting extensions have been given by Browder (1983), Nussbaum (1972), Fitzpatrick (1970, 1974), Petryshyn (1974) and other authors.
In this thesis a degree function is constructed for mappings of monotone type in Orlicz-Sobolev spaces using the Galerkin approximation method as in [Bull. Am. Math. Soc. 9, 1-39 (1983; Zbl 0533.47053)]. Some interesting applications to nonlinear equations are given.
In this thesis a degree function is constructed for mappings of monotone type in Orlicz-Sobolev spaces using the Galerkin approximation method as in [Bull. Am. Math. Soc. 9, 1-39 (1983; Zbl 0533.47053)]. Some interesting applications to nonlinear equations are given.
Reviewer: J.M.Ayerbe (Sevilla)
MSC:
| 47H11 | Degree theory for nonlinear operators |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
